We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information on hadron structure constants by connecting information from complementary scattering processes. We consider the real and virtual Compton scattering processes off the proton, and summarize recent advances in the DR analysis of experimental data to extract the proton polarizabilities, in comparison with alternative studies based on chiral effective field theories. We discuss a multipole analysis of real Compton scattering data, along with a DR fit of the energy-dependent dynamical polarizabilities. Furthermore, we review new sum rules for the double-virtual Compton scattering process off the proton, which allow for model independent relations between polarizabilities in real and virtual Compton scattering, and moments of nucleon structure functions. The information on the double-virtual Compton scattering is used to predict and constrain the polarizability corrections to muonic hydrogen spectroscopy.
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